Measurement
A triangle has sides of lengths 6, 10 and 11. An equilateral triangle has the same perimeter. What is the side length of the equilateral triangle?
9
Only one of the digits in the year 2018 is a prime number. How many years will pass till the next year when all of the digits in the year number are prime numbers?
204
The product of two numbers is 36 and their sum is 37. What is their difference?
35
Poppy has $20. Each of her four sisters has $10. How many dollars does Poppy have to give to each of her sisters so that each of the girls have the same amount of money?
$2
A group of friends stand in a circle. Zac is fourth on the left from Yasuo and the seventh on the right from Yasuo. How many friends are in the group?
11
A cyclist rides at 5 m per second. The wheels of his bicycle have a circumference of 125 cm. How many complete turns does the wheel make in 5 seconds?
20 turns
When Darius begins a journey, his car odometer shows a palindromic number 29792 km. At the end of the journey, 3 hours later, the odometer shows another palindromic number. Darius is a responsible driver, respects the traffic rules and knows that his average speed cannot exceed 100 km/h. What is the maximum average speed that Darius could have recorded?
211/3 km/h
How much faster does the second hand of a circular clock make one complete rotation compared to the hour hand of the same clock?
720 times
Alistar and Garen each have several dollars. If Alistar gives $6 to Garen, they will have the same amount of money. If Alistar gives a half of his money to Garen, then Garen will have $8 more than Alsitar will have. How much money in total do the boys have?
28
In 16 years, Tristana will be five times older than she was four years ago. In how many years will Tristana celebrate her 16th birthday?
7 years
Katarina added the lengths of three sides of a rectangle and got 44cm. Jax added the lengths of three sides of the same rectangle and got 40cm. What is the perimeter of the rectangle?
56 cm
The neighbours of a two-digit number are a prime number and a perfect square (a square of a whole number). How many two-digit numbers are there with this property?
5
A soccer club owns five identical mowers. It takes 10 hours to mow the grass of the soccer field using two of the mowers. How long does it take to mow the grass of the same field using all five mowers?
4 hours
Annie, Brand and Camille went shopping. Brand spent only 15% of what Camille spent. However, Annie spent 60% more than Camille. Together, they spent $55. How much did Annie spend?
$32
Four friends, Elise, Irelia, Rakan and Zoe are 3, 8, 12 and 14 years old, although not necessarily in that order. The sum of the ages of Zoe and Elise is divisible by 5. The sum of the ages of Zoe and Rakan is also divisible by 5. How old is Irelia?
14
In the triangle ABC of area 120 square centimeters, the ratio between the length of one side and the corresponding height is 3:5. What is this height, in cm?
20 cm
Using only the digits 1, 2, 3, 4, and 5 exactly once, Janna wrote several prime numbers less than 100. She also noticed that there was more than one way to do that, with one prime number being always in the list. What is this number?
41
Every asterisk in the equation:
2 ∗ 0 ∗ 1 ∗ 5 ∗ 2 ∗ 0 ∗ 1 ∗ 5 ∗ 2 ∗ 0 ∗ 1 ∗ 5 = 0
is to be replaced with either + or − so that the equation is correct. What is the smallest number of asterisks that must be replaced with +?
2
The average allowance of 6 friends is $60. When two new friends, Riven and Shen, join the group of friends, the average allowance of the group decreases to $58. If Riven's allowance is $8 more than Shen's, what is Riven's allowance?
$56
Ten children are lined up from tall to small. They have to be lined up from small to tall. This will be achieved by a number of interchanges of two children next to each other. How many interchanges are needed?
45
The measures of the angles in a triangle, in degrees, are three different integers. What is the minimum possible sum of its smallest and largest angles?
91 degrees
Consider a rectangle whose side lengths are prime numbers and the perimeter equals 100. How many different values can the area of such rectangle take?
4
There are three candidates for one position as class supervisor and 130 students are voting. Caitlyn has 24 votes so far, while Lux has 29 votes and Ahri has 37 votes. How many more votes does Ahri need in order to receive more votes than any of the other two candidates?
17
Captain Fizz and his pirate crew dug up several gold coins. They are dividing the coins amongst themselves so that each person gets the same number of coins. If there were four fewer pirates, then each person would get 10 more coins. However, if there were 50 fewer coins, then each person would get 5 fewer coins. How many coins did they dig up?
150
Quinn and Nunu are practicing for their race on a 720 m circular track. They run in opposite directions, each at a constant speed. Quinn needs 4 minutes to complete the full loop and Nunu needs 5 minutes. How many meters does Nunu travel between two consecutive meetings with Quinn?
320 m